Summary: Improved Modular Termination Proofs Using
Dependency Pairs
Ren’e Thiemann, J˜urgen Giesl, Peter Schneider­Kamp
LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
{thiemann|giesl|psk}@informatik.rwth­aachen.de
Abstract. The dependency pair approach is one of the most powerful
techniques for automated (innermost) termination proofs of term rewrite
systems (TRSs). For any TRS, it generates inequality constraints that
have to be satisfied by well­founded orders. However, proving innermost
termination is considerably easier than termination, since the constraints
for innermost termination are a subset of those for termination.
We show that surprisingly, the dependency pair approach for termination
can be improved by only generating the same constraints as for innermost
termination. In other words, proving full termination becomes virtually
as easy as proving innermost termination. Our results are based on split­
ting the termination proof into several modular independent subproofs.
We implemented our contributions in the automated termination prover
AProVE and evaluated them on large collections of examples. These ex­
periments show that our improvements increase the power and e#ciency
of automated termination proving substantially.